Specification Testing for Transformation Models

Published in Journal of Econometrics https://doi.org/10.1016/j.jeconom.2014.09.008</p

Evaluating Value-at-Risk Models via Quantile Regressions

We propose an alternative backtest to evaluate the performance of Value-at-Risk (VaR) models. The presented methodology allows us to directly test the performance of many competing VaR models, as well as identify periods of an increased risk exposure based on a quantile regression model (Koenker & Xiao, 2002). Quantile regressions provide us an appropriate environment to investigate VaR models, since they can naturally be viewed as a conditional quantile function of a given return series. A Monte Carlo simulation is presented, revealing that our proposed test might exhibit more power in comparison to other backtests presented in the literature. Finally, an empirical exercise is conducted for daily S&P500 return series in order to explore the practical relevance of our methodology by evaluating five competing VaRs through four different backtests.

Quantum entanglement

All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended) presentation, updated references, minor changes, submitted to Rev. Mod. Phys

Entanglement Theory and the Quantum Simulation of Many-Body Physics

In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum many-body phenomena. In the first part we introduce a new approach to the study of entanglement by considering its manipulation under operations not capable of generating entanglement and show there is a total order for multipartite quantum states in this framework. We also present new results on hypothesis testing of correlated sources and give further evidence on the existence of NPPT bound entanglement. In the second part, we study the potential as well as the limitations of a quantum computer for calculating properties of many-body systems. First we analyse the usefulness of quantum computation to calculate additive approximations to partition functions and spectral densities of local Hamiltonians. We then show that the determination of ground state energies of local Hamiltonians with an inverse polynomial spectral gap is QCMA-hard. In the third and last part, we approach the problem of quantum simulating many-body systems from a more pragmatic point of view. We analyze the realization of paradigmatic condensed matter Hamiltonians in arrays of coupled microcavities, such as the Bose-Hubbard and the anisotropic Heisenberg models, and discuss the feasibility of an experimental realization with state-of-the-art current technology.Comment: 230 pages. PhD thesis, Imperial College London. Chapters 6, 7 and 8 contain unpublished materia

Instrumental Variables: An Econometrician's Perspective

I review recent work in the statistics literature on instrumental variables methods from an econometrics perspective. I discuss some of the older, economic, applications including supply and demand models and relate them to the recent applications in settings of randomized experiments with noncompliance. I discuss the assumptions underlying instrumental variables methods and in what settings these may be plausible. By providing context to the current applications, a better understanding of the applicability of these methods may arise.Comment: Published in at http://dx.doi.org/10.1214/14-STS480 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Non-classicalities in quantum walks and an axiomatic approach to quantum realism

Orientador: Prof. Dr. Renato Moreira AngeloTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Física. Defesa : Curitiba, 26/05/2022Inclui referências: p. 125-137Resumo: No cerne das estranhezas da mecânica quântica estão a superposição de estados e a complementariedade de Bohr, noções conflitantes com a nossa percepção de realidade física macroscópica. Recentemente, uma hipótese de realismo foi formulada assumindo que a mecânica quântica constitui uma teoria física completa. Esta hipótese parte de uma ideia que é compartilhada também por defensores do Darwinismo Quântico: de que a codificação de informação sobre um dado observável em um grau de liberdade físico é uma condição necessária para que tal observável se torne um elemento de realidade física. Nesta tese, nós exploramos tal proposta de realismo dentro da teoria quântica em duas partes. Na Parte I nós estudamos um sistema físico conhecido como caminhadas quânticas e analisamos como se dá a emergência de realidade física objetiva de observáveis de spins durante a evolução de diversas não-classicalidades entre os subsistemas, a citar, não-localidade de Bell, direcionamento quântico, emaranhamento, discórdia quântica, irrealismo e não-localidade baseada em realismo. Motivados por esta análise, nós buscamos, na Parte II, nos aprofundar ainda mais no conceito de realismo dentro da mecânica quântica. Tomando a ideia de fluxo de informação do sistema para o ambiente como condição necessária para a emergência de realidade física, nós construímos uma axiomatização para o aqui chamado realismo quântico-em oposição ao realismo clássico. Nossa estratégia consiste em listar alguns princípios motivados fisicamente que sejam capazes de caracterizar o realismo quântico de maneira independente de "métrica". Introduzimos alguns critérios que definem monótonas e medidas de realidade e, em seguida, procuramos potenciais candidatos dentro de algumas teorias da informação célebres (entropias de von Neumann, Rényi e Tsallis) e também por medidas geométricas (distâncias do traço, Hilbert-Schmidt, Bures e Hellinger). Construímos explicitamente algumas classes de quantificadores entrópicos e geométricos, entre os quais que alguns satisfazem todos os axiomas propostos e, portanto, podem ser tomados como estimativas fiéis para o grau de realidade (ou definidade) de um dado observável físico. Nós esperamos que nossa estrutura possa oferecer uma base formal para futuras discussões sobre aspectos fundamentais da mecânica quântica.Abstract: At the heart of the strangeness of quantum mechanics are the superposition of states and Bohr's complementarity, notions that are in conflict with our perception of macroscopic physical reality. Recently, a realism hypothesis has been formulated assuming that quantum mechanics constitutes a complete physical theory. This hypothesis starts from an idea that is also shared by supporters of Quantum Darwinism: that the encoding of information about a given observable in a physical degree of freedom is a necessary condition for such an observable to become an element of physical reality. In this thesis, we explore such a proposal of realism within quantum theory into two parts. In Part I we study a physical system known as quantum walks and analyze how the emergence of objective physical reality of spin observables occurs during the evolution of several non-classicalities between subsystems, namely, Bell nonlocality, quantum steering, entanglement, quantum discord, irrealism, and realism-based nonlocality. Motivated by this analysis, we seek, in Part II, to get even further into the concept of realism within quantum mechanics. Taking the idea of information flow from the system to the environment as a necessary condition for the emergence of physical reality, we build an axiomatization for the here called quantum realism-as opposed to classical realism. Our strategy is to list some physically motivated principles that are capable of characterizing quantum realism in a "metric" independent way. We introduce some criteria that define monotones and measures of reality and then we look for potential candidates within some famous information theories (von Neumann, Rényi and Tsallis entropies) and also by geometric measures (trace, Hilbert- Schmidt, Bures, and Hellinger distances). We explicitly build some classes of entropic and geometric quantifiers, among which some satisfy all the proposed axioms and, therefore, can be taken as faithful estimates for the degree of reality (or definiteness) of a given physical observable. We hope that our framework can provide a formal basis for future discussions of fundamental aspects of quantum mechanics

Identification and estimation of nonlinear regression models using control functions

According to Blundell and Powell (2003), the development of strategies to identify and estimate certain parameters or even entire functions of regression models under endogeneity has arguably been one of the main contributions of microeconometrics to the statistical literature. The term endogeneity, in this context, refers to a correlation between observable regressor(s) and model unobservable(s), which can arise for multiple reasons such as, among others, omitted variables, measurement error, unobserved heterogeneity, or simultaneous causality. Whereas linear identification and estimation techniques to address endogeneity date back as far as 1928 (Stock and Trebbi, 2003), advances in the field of nonlinear models are much more recent: nonlinear parametric models under endogeneity only came under investigation during the 1970s and 1980s (e.g. Ameniya, 1974; Hansen, 1982), and it was not until the mid 1990s that models of (partially) unknown functional form were considered

Aspects of Entanglement Entropy in Algebraic Quantum Field Theory

In this thesis, we study aspects of entanglement theory of quantum field theories from an algebraic point of view. The main motivation is to gain insights about the general structure of the entanglement in QFT, towards a definition of an entropic version of QFT. In the opposite direction, we are also interested in exploring any consequence of the entanglement in algebraic QFT. This may help us to reveal unknown features of QFT, with the final aim of finding a dynamical principle which allows us to construct non-trivial and rigorous models of QFT. The algebraic approach is the natural framework to define and study entanglement in QFT, and hence, to pose the above inquiries. After a self-contained review of algebraic QFT and quantum information theory in operator algebras, we focus on our results. We compute, in a mathematically rigorous way, exact solutions of entanglement measures and modular Hamiltonians for specific QFT models, using algebraic tools from modular theory of von Neumann algebras. These calculations show explicitly non-local features of modular Hamiltonians and help us to solve ambiguities that arise in other non-rigorous computations. We also study aspects of entanglement entropy in theories having superselection sectors coming from global symmetries. We follow the algebraic perspective of Doplicher, Haag, and Roberts. In this way, we find an entropic order parameter that "measures" the size of the symmetry group, which is made out of a difference of two mutual informations. Moreover, we identify the main operators that take account of such a difference, and we obtain a new quantum information quantity, the entropic certainty relation, involving algebras containing such operators. This certainty relation keeps an intrinsic connection with subfactor theory of von Neumann algebras.Comment: PhD thesis (2019), 344 pages, 20 figure